Well I finally got it figured out today... it turns out a lot of that stuff isn't off that 20A circuit in the PDC. That circuit really only has a couple things on it:
Fuse 6 in the interior fuse block
Fuse 7 in the interior fuse block
An illumination wire for the factory radio
Because both fuses 6 and 7 were fine on my jeep, that means that the problem is somewhere before the power got to those fuses.
But since it only happened when the headlight switch was turned on, that means that the wiring from the 20A (in the PDC) up to the headlight switch, was fine and that the problem was somewhere between the headlight switch and those fuses.
That only leaves a little bit of wire to check out with the multimeter... and when I found no shorts in those 2 sections of wire I knew the problem had to be the radio illumination wire that came off the headlight switch.
The FSM showed the radio illumination wire to be Black and Yellow so I pulled the dash apart at the radio to find that wire.
A little more poking around and I found that the wire had been pinched from when I was doing some work on my dash and it was shorting out. A little heat shrink and a butt-splice fixed the problem nicely and everything is working great again.
I am attaching a diagram I made of that circuit for future reference for anyone who is having a similar problem.
Circuit F34 is that 20A fuse in the PDC.
The rest should all be pretty self-explanatory.